椭圆轨道绳系卫星系统释放的类反步法控制

Backstepping-like nonlinear control for the deployment of tethered satellite system in elliptical orbits

摘要:

为解决椭圆轨道上绳系卫星系统的稳定和快速释放问题,在传统反步法的基础上,提出了一种类反步法的非线性控制方法.与传统反步法仅适应于严格反馈系统不同,提出的类反步法非线性控制方法不仅可以应用于非严格反馈系统,并且能够充分地利用系统的非线性模型来改善控制效果.首先,基于拉格朗日力学原理,建立了椭圆轨道上绳系卫星系统释放过程的动力学模型,并通过一种新型的量纲为1的变换对动力学模型进行化简,得到了量纲为1的卫星系统模型；其次,设计了一种类反步非线性控制方法以应对绳系卫星系统模型中的耦合特性,并采用Lyapunov函数验证了各系统状态的渐进稳定性能；最后,设计了绳系卫星系统释放过程的非线性控制和PID控制的数值仿真实验,通过对比验证了所提出的类反步法非线性控制方法的有效性.仿真结果表明,所提出的类反步法控制方案不仅可以稳定、高效地控制椭圆轨道上绳系卫星系统的释放过程；而且相对比传统的PID控制方案所取得的控制效果更优.

Abstract:

To solve the stability and fast deployment problems of tethered satellite system (TSS) in elliptical orbits, a novel backstepping-like nonlinear control algorithm was proposed based on the traditional backstepping control method. Different from the traditional backstepping method which is only suitable for strict feedback systems, the proposed backstepping-like nonlinear control has a wider range of application that it can be applied to the control of non-strict feedback systems and can improve the control performance with effective use of the nonlinear model. First, the nonlinear dynamic model for the deployment of TSS in elliptical orbit was established based on the Lagrangian mechanics, and the dimensionless system model was further simplified with a new dimensionless transformation. Then, by utilizing the simplified model, a backstepping-like nonlinear control method was proposed to deal with the coupling characteristics of the system model, and the Lyapunov function was adopted to verify the asymptotic stability of the system states. Finally, simulation experiments of non-linear control and PID control for the deployment of TSS in elliptical orbit were carried out, and the effectiveness of the proposed backstepping-like nonlinear control was verified by comparison. Simulation results show that the proposed method deployed the tether satellite effectively and stably and achieved better performance than the classical PID controller.